Formulation of a new dynamic slip wall model in a Consistent Discontinuous Galerkin Framework

Slip wall modeling (Bose et al. 2014, Phy. Fluids 26(1), 015104; Bae et al. 2019, J. Fluid Mech. 859, 400-432) has been suggested as a promising approach to realize LES as a feasible computational tool for practically relevant high Reynolds number flows. In this work, building on the slip wall model of Pradhan and Duraisamy 2023 (J. Fluid Mech. 955, A6), we propose a new modeling procedure in which the dynamic part of the model is based on a modified form of Germano identity, and makes use of a model for the slip wall model coefficients obtained using an optimal finite-element projection framework. The dynamic slip wall model is tightly integrated with Discontinuous-Galerkin (DG) operators. A sharp modal cut-off filter is used as the test filter for the dynamic procedure. The performance of the new model is validated using a series of statistically stationary turbulent flows at high Reynolds numbers. Numerical experiments show that, similar to traditional wall-stress models, grid convergence studies are possible for the slip wall model provided the size of the element adjacent to the wall is fixed. The results show that the new dynamic model is able to consistently predict mean velocity profiles along with the Reynolds normal and shear stresses that match with the available DNS for various under-resolved coarse LES meshes.